Japanese Patent Publication No. 2802061 discloses an endoscope with an observation optical system that contains a variable transmittance optical element known as an etalon wherein the etalon includes facing optical surfaces that are separated by an air gap spacing. The air gap spacing may be controlled by applying a voltage to a piezoelectric element so as to change the transmittance characteristics of the etalon.
FIG. 16 is an illustration showing the basic structure of such an etalon. The etalon shown in FIG. 16 comprises two substrates 35X-1 and 35X-2 having, on their facing surfaces, reflective coatings 35Y-1 and 35Y-2 with an air gap spacing d between the coatings on the facing surfaces. Of light entering from the substrate 35X-1, light of a very narrow range of wavelengths exits from reaches the substrate 35X-2 because of multiple beam interference that occurs between the reflective coatings 35Y-1 and 35Y-2.
As shown in FIG. 17, the peak transmittance wavelength of the etalon is shifted from Ta to Tb as the magnitude of the air gap spacing d is changed. A piezoelectric element can be used as a means to move the substrates to thereby change the magnitude of the air gap spacing d.
An etalon periodically exhibits peak transmittances for specific wavelengths of light as the air gap spacing d is changed. Generally, the spectral transmittance of an etalon is expressed by the following Equation (1):T=1/{1+[4R sin2(2πnd cos θ/λ)/(1−R)2]}  Equation (1)where
T is the transmittance of the etalon for a given wavelength of light incident onto the etalon;
R is the reflectance of the reflective coatings;
n is the refractive index of the material, which generally is air—the refractive index of which is 1, between the substrates with attached coatings;
d is the air gap spacing between the substrates with attached coatings;
θ is the angle of incidence of the light onto the etalon, as measured from the surface normal; and
λ is the wavelength of light incident onto the etalon.
The wavelengths for which an etalon has periodic peak spectral transmittances T occur where the following Equation (2) is satisfied:m=2nd cos θ/λmax  Equation (2)where
m is an integer,
n, d, and θ are as defined above, and
λmax is one of the periodic wavelengths for which the etalon has a peak transmittance.
When light is incident onto an etalon at zero degrees (i.e., parallel to the surface normal), the etalon has peak spectral transmittances T for light of wavelengths (2/m) d. In this way, the wavelength of light that is transmitted through the etalon can be selected by changing the air gap spacing d. If an etalon is provided in the imaging optical system of an endoscope, observation images consisting of light having a desired wavelength can be obtained.